Question

(a) plot ( 1 + sqrt{5} ) and ( pi ) on the decimal number line. note that you can use the calculator. (b) based on your answer above, compare ( 1 + sqrt{5} ) and ( pi ) using ( < ), ( > ), or ( = ). ( 1 + sqrt{5} square pi )

Explanation:

Step1: Calculate $1+\sqrt{5}$

$\sqrt{5} \approx 2.236$, so $1+\sqrt{5} \approx 1 + 2.236 = 3.236$

Step2: Recall value of $\pi$

$\pi \approx 3.1416$

Step3: Compare the two values

$3.236 > 3.1416$

Step4: Plot on number line

Mark $3.236$ (for $1+\sqrt{5}$) between 3.2 and 3.3, and $3.1416$ (for $\pi$) between 3.1 and 3.2 on the given number line.

Answer:

(a) On the provided number line:

• Mark $\pi \approx 3.14$ between 3.1 and 3.2, closer to 3.1
• Mark $1+\sqrt{5} \approx 3.24$ between 3.2 and 3.3, closer to 3.2

(b) $1+\sqrt{5} > \pi$